May's party is short of the 326 it needed for an outright majority and fairly down from the 330 seats it had before the election.
But after seeing her Commons majority wiped out on a night of humiliation for the Tories, she was left with limited room for manoeuvre when it came to re-shaping her top team.
She has already sought permission from the Queen at Buckingham Palace about forming a government in alliance with the DUP.
The party, which returned 10 MPs to Westminster, opposes same-sex marriage and is anti-abortion - abortion remains illegal in Northern Ireland, except in specific medical cases.
Ruth Davidson, the Conservative leader in Scotland, said she had asked May for assurances that there would be no attack on gay rights after a deal with the DUP.
"One of them is country, one of the others is LGBTI rights".
"I make no apology for saying that the DUP will always strive for the best deal for Northern Ireland and its people".
The DUP wants no extension to Northern Ireland's limitations on terminations, which restrict the procedure to when a woman's life is at risk or there is a permanent or serious risk to her mental or physical health.
KHALAF: Well, given the spectacular fiasco of the elections and the fact that Theresa May ran on a platform of a hard Brexit, I think one can assume that she no longer has a mandate for a hard Brexit.
Mr Wilson described Mr Trump's decision last month to withdraw the U.S. from the Paris Agreement on climate change as "very wise", saying the accord was "totally flawed and pointless".
Corbyn, speaking after being re-elected in Islington North, said it was time for Mrs May to "make way" for a government that would be "truly representative of the people of this country".
Socialist group leader Gianni Pittella called the election result a "disaster" for May and called for her resignation.
Among Tory MPs there was fury at the way a 20-point opinion poll lead at the start of the campaign had been thrown away in an election which she did not need to call for another three years.
And in the Commons, she will require total loyalty from her backbenchers, given her precarious political position. But she is also a democrat.
The PM's gamble of calling a snap election to increase her majority had backfired in spectacular fashion, so could the pair be casualties or will she stick by them? "We are the largest party, we can govern".
However devolved delivery means there is likely to be little conflict with any health and social care reform in England that the Conservatives choose to progress following the election campaign's embarrassing U-turn on capping social care costs.
McDonnell also said Labour would not do a coalition deal with any other party.
The BBC reported that there have been calls among senior members of the Conservative party to have the two sacked during the weekend or that Prime Minister May would face internal struggles within her party on Monday.
They are expected to work with smaller parties to form a majority, while May plans to stay on as prime minister.